A Closed-Form Solution for Optimal Mean-Reverting Trading Strategies

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See all articles by Alex Lipton

Alex Lipton

Hebrew University of Jerusalem; Massachusetts Institute of Technology (MIT)

Marcos Lopez de Prado

Cornell University - Operations Research & Industrial Engineering; True Positive Technologies

Date Written: February 8, 2020

Abstract

When prices reflect all available information, they oscillate around an equilibrium level. This oscillation is the result of the temporary market impact caused by waves of buyers and sellers. This price behavior can be approximated through an Ornstein-Uhlenbeck (OU) process.

Market makers provide liquidity in an attempt to monetize this oscillation. They enter a long position when a security is priced below its estimated equilibrium level, and they enter a short position when a security is priced above its estimated equilibrium level. They hold that position until one of three outcomes occur: (1) they achieve the targeted profit; (2) they experience a maximum tolerated loss; (3) the position is held beyond a maximum tolerated horizon.

All market makers are confronted with the problem of defining profit-taking and stop-out levels. More generally, all execution traders holding a particular position for a client must determine at what levels an order must be fulfilled. Those optimal levels can be determined by maximizing the trader's Sharpe ratio in the context of OU processes via Monte Carlo experiments. This paper develops an analytical framework and derives those optimal levels by using the method of heat potentials.

Keywords: Optimal trading strategy, Heat potentials, Ornstein-Uhlenbeck process, mean-reversion

JEL Classification: G0, G1, G2, G15, G24, E44

Suggested Citation

Lipton, Alex and López de Prado, Marcos, A Closed-Form Solution for Optimal Mean-Reverting Trading Strategies (February 8, 2020). Available at SSRN: https://ssrn.com/abstract=

Alex Lipton

Hebrew University of Jerusalem ( email )

Mount Scopus
Jerusalem, IL Jerusalem 91905
Israel

Massachusetts Institute of Technology (MIT) ( email )

77 Massachusetts Avenue
50 Memorial Drive
Cambridge, MA 02139-4307
United States

Marcos López de Prado (Contact Author)

Cornell University - Operations Research & Industrial Engineering ( email )

237 Rhodes Hall
Ithaca, NY 14853
United States

HOME PAGE: http://www.orie.cornell.edu

True Positive Technologies ( email )

NY
United States

HOME PAGE: http://www.truepositive.com

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